To deal with computationally intractable problems, the practical approach is to use approximation algorithms or parameterized algorithms. Algorithms that output near-optimal solutions in polynomial time are precisely the class of approximation algorithms. It is known [1]}, that DS has an approximation algorithm with approximation ratio \((1+\ln n)\)  on general graphs. On the negative side, DS does not admit \((1-\epsilon )\ln n \)  on general graphs, for any \(\epsilon >0\)  unless NP \(\subseteq \)  DTIME (\(n^{O(\log \log n)}\) ) [2]}. In this paper, restricted to split graphs, we prove that DS exhibits \(2-\frac{1}{|I|}\) -approximation algorithm.
